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I have a need to compute the apparent azimuth and elevation angles as well as the sub-lunar lat/lon for a given date/time. The az/el angles I get generally agree with other sources (MoonCalc.org, Horizons, etc.) but there are not good comparison sources for the sub-lunar lat/lon. More importantly, I doubt the lat/lon I get using the dec/ra values because the ra barely changes over long time frames.

Here is the basic call I am making:

roc.date='2018/1/1 01:00:00'
moon=ephem.Moon(roc)
print('rocMoonTest: %s UTC-4, lat/lon = %0.4f [+N], %0.4f [+E]' %
    (roc.date, math.degrees(roc.lat), math.degrees(roc.lon)))
print('Moon dec/ra     = %s [+N], %s [+W]' % (moon.dec, moon.ra ))
print('Moon a_dec/a_ra = %s [+N], %s [+W]' % (moon.a_dec, moon.a_ra ))
print('Moon g_dec/g_ra = %s [+N], %s [+W]' % (moon.g_dec, moon.g_ra ))
print('Moon az/el      = %0.4f, %0.4f' %
    (math.degrees(moon.az), math.degrees(moon.alt)))

And then I iterate on that every 3 hours. Below is the output:

rocMoonTest: 2018/1/1 01:00:00 UTC-4, lat/lon = 43.0000 [+N], -78.0000 [+E]
Moon dec/ra     = 18:53:07.1 [+N], 5:43:03.33 [+W]
Moon a_dec/a_ra = 19:22:21.3 [+N], 5:39:38.43 [+W]
Moon g_dec/g_ra = 19:22:44.7 [+N], 5:40:41.41 [+W]
Moon az/el      = 105.3953, 43.0670

rocMoonTest: 2018/1/1 04:00:00 UTC-4, lat/lon = 43.0000 [+N], -78.0000 [+E]
Moon dec/ra     = 19:07:55.4 [+N], 5:49:00.24 [+W]
Moon a_dec/a_ra = 19:32:24.2 [+N], 5:47:42.22 [+W]
Moon g_dec/g_ra = 19:32:35.1 [+N], 5:48:45.29 [+W]
Moon az/el      = 169.5907, 65.8406

rocMoonTest: 2018/1/1 07:00:00 UTC-4, lat/lon = 43.0000 [+N], -78.0000 [+E]
Moon dec/ra     = 19:13:15.7 [+N], 5:54:49.89 [+W]
Moon a_dec/a_ra = 19:41:07.2 [+N], 5:55:47.50 [+W]
Moon g_dec/g_ra = 19:41:05.5 [+N], 5:56:50.65 [+W]
Moon az/el      = 246.5737, 49.4664

As expected and as verified by the az/el angles, the moon swings from East to West as the earth rotates and reaches a peak altitude somewhere during the period. However, none of the various dec/ra values change significantly. Over this 6 hour span, I would expect to see approximately a 6 hour change in the ra. Obviously, when I use any of these ra values to compute the longitude, I get the wrong answer. It appears the reference frame for dev/ra is not rotating with the earth. However, the docs indicate that I should expect it to.

Anyone care to explain where I went wrong in my understanding of the various right ascension variables and what the most direct way is to compute the sub-lunar lat/lon? Note, I would rather avoid using an approach that rotates the apparent az/el position into geodetic lat/lon.

SDBrown
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  • Could you quote more specifically the documentation that describes the right ascension (RA) as changing as the Earth turns? My own understanding is that the right ascension of an object is its position against the stars, so it would take ~1 month for the Moon's right ascension to go through 360°. – Brandon Rhodes Sep 15 '18 at 16:47
  • Brandon, this was the key misunderstanding on my behalf. Not coming from the uplooking astronomy community but rather the downlooking remote sensing community, I was not aware of the reference frame for right ascension and that it isn't Earth fixed. It appears incorporating the sidereal time is the missing ingredient in my calculation. – SDBrown Sep 15 '18 at 17:02
  • I'm glad we tracked down the source of confusion and you can more forward again! I'll write up a little answer, then, so that other folks with the same question can easily find the answer in the future. – Brandon Rhodes Sep 16 '18 at 18:54

3 Answers3

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The measurement “Right Ascension" is made not against the rotating surface of the Earth, but against the fixed stars of the sky — it is a kind of longitude but whose origin is the point on a star chart where the two great “equators of the sky,” the Earth’s equator and the “Solar System's equator”, the Ecliptic (which is not truly the Solar System equator because it's the plane of the Earth's orbit, rather than the weighted average of all planetary orbits), cross.

Since the point of their crossing itself moves as the ages pass, the system of Right Ascension is very slightly different every year, and very different across centuries and millenia. So Right Ascension and declination (celestial latitude) always have to be specified relative to some date, some exact moment like B1950 or J2000.

There is now a fixed coordinate system for RA and dec that doesn't move, the ICRS, which is oriented like J2000 but is defined using the positions of quasars which (we assume) won't move measurably within the lifetime of our species.

Brandon Rhodes
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regarding this part of your question

what the most direct way is to compute the sub-lunar lat/lon?

Here is my code to calculate the sublunar point. 

greenwich = ephem.Observer()
greenwich.lat = "0"
greenwich.lon = "0"
greenwich.date = datetime.utcnow()

#add Moon Sub Solar Point
moon = ephem.Moon(greenwich)
moon.compute(greenwich.date)
moon_lon = math.degrees(moon.ra - greenwich.sidereal_time() )
# map longitude value from -180 to +180 
if moon_lon < -180.0 :
  moon_lon = 360.0 + moon_lon 
elif moon_lon > 180.0 :
  moon_lon = moon_lon - 360.0

moon_lat = math.degrees(moon.dec)
print "moon Lon:",moon_lon, "Lat:",moon_lat

Hope that helps. I also use the same approach to calculate the sub-solar point. Works great for me.

EDIT: Yes... latitude of Greenwich is set to zero BECAUSE it doesn't matter at all for this calculation.

Liam Kennedy
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You might reinforce your thinking in the direction of this approach by taking a look at this other link:

Computing sub-solar point

Which gives basically the same solution, but for the sub_solar_point, also from Liam Kennedy (where he gave a non zero Lat for Greenwich), and also with an answer from Brandon Rhodes who wrapped the xephem library in python to give us pyephem, and until recently was actively maintaining it. Brandon is now focusing more on his next iteration, a pure python library called skyfield, which uses the latest available ephemeris with a more intuitive API.

https://pypi.org/project/skyfield/

https://rhodesmill.org/skyfield/installation.html

Although I can not contribute it now, might I suggest a comparison of the results of pyephem and skyfield, perhaps in a matplotlib figure or two, IOW, just how different/improved might be the results from skyfield?

always_learning
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